Exact solutions in general relativity

Null dust solution

In mathematical physics, a null dust solution (sometimes called a null fluid) is a Lorentzian manifold in which the Einstein tensor is null. Such a spacetime can be interpreted as an exact solution of Einstein's field equation, in which the only mass–energy present in the spacetime is due to some kind of massless radiation. (Wikipedia).

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Null space of a matrix

In this video I start to discuss the idea of the null space of a matrix. In these situations, the right-hand side of all the equations in the linear system is equal to zero. There is the trivial solution, where all the elements of the solution is zero. We are more interested in the spec

From playlist Introducing linear algebra

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Null Space: Is a Vector in a Null Space? Find a Basis for a Null Space

This video explains how to determine if a vector is in a null space and how to find a basis for a null space.

From playlist Column and Null Space

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Null space of a matrix using sympy

In this video I give a brief overview of the null space of a matrix and how to calculate (y hand) the column vectors that will make up the null space of the column. This becomes much easier in sympy, by simply using the nullspace function. If you want to learn more about the null space o

From playlist Modern linear algebra using Python instead of a textbook

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Null space of a matrix example

In today's lecture I work through an example to show you a well-known pitfall when it comes to the null space of a matrix. In the example I show you how to create the special cases and how to use them to represent the null space. There is also a quick look at the NullSpace function in Ma

From playlist Introducing linear algebra

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Null points and null lines | Universal Hyperbolic Geometry 12 | NJ Wildberger

Null points and null lines are central in universal hyperbolic geometry. By definition a null point is just a point which lies on its dual line, and dually a null line is just a line which passes through its dual point. We extend the rational parametrization of the unit circle to the proj

From playlist Universal Hyperbolic Geometry

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Prove a Null Space is a Subspace

This video provides a basic proof that a null space is a subspace.

From playlist Column and Null Space

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The Largest and Smallest Values for the Rank and Nullity of a Matrix (3 x 5)

This video explains how to determine the largest and smallest possible values for the rank and nullity of a 3 by 5 matrix.

From playlist Column and Null Space

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Plenary Lectures by Robert Kirshner, Mihalis Dafermos

PROGRAM: INTERNATIONAL CONFERENCE ON GRAVITATION AND COSMOLOGY DECEMBER 14-19, 2011 GOA, INDIA ORGANIZERS: Subhabrata Majumdar, B.S. Sathyaprakash, Tejinder Pal Singh and Tarun Souradeep DATE & TIME: 15 December 2011 to 19 December 2011 VENUE: IUCAA, Mobor Beach, Goa International Confer

From playlist International Conference on Gravitation and Cosmology 2011

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Cécile Huneau: High frequency back reaction for the Einstein equations

Abstract: It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency, yield at the limit to a non trivial contribution which corresponds to the presence of an energy impulsion tens

From playlist Mathematical Physics

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Lars Andersson - Geometry and analysis in black hole spacetimes (Part 2)

Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity. Following a brief i

From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

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Review of Ax=b for Differential Equations

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Partial Differential Equations

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Statistics: Ch 9 Hypothesis Testing (3 of 35) What is the "Null Hypothesis"?

Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 The alternative hypothesis gives a different (or alternate) explanation about the product, the design, of the capability that indicat

From playlist STATISTICS CH 9 HYPOTHESIS TESTING

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Math 060 092517 Adjoint Matrix, Subspaces

Definition of adjoint matrix. Connection with inverse matrix (via "wrong cofactor lemma"). Example. Subspaces: recall main theorem (how verify a subset is a subspace: check closure under vector space operations). Null space. The null space is a subspace. Example of determining the n

From playlist Course 4: Linear Algebra (Fall 2017)

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Limiting Curvature in the Very Early Universe by Jerome Quintin

PROGRAM: PHYSICS OF THE EARLY UNIVERSE - AN ONLINE PRECURSOR ORGANIZERS: Robert Brandenberger (McGill University, Montreal, Canada), Jerome Martin (Institut d'Astrophysique de Paris, France), Subodh Patil (Instituut-Lorentz for Theoretical Physics, Leiden, Netherlands) and L Sriramkumar (

From playlist Physics of The Early Universe - An Online Precursor

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20. Supernovae Ia and Vacuum Energy Density

MIT 8.286 The Early Universe, Fall 2013 View the complete course: http://ocw.mit.edu/8-286F13 Instructor: Alan Guth In this lecture, the professor first talked about supernovae type Ia; summarized the age of the universe and radiation flux versus redshift; and talked about vacuum energy d

From playlist The Early Universe by Prof. Alan Guth

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Entropy Bounds, Light-sheets, and the Holographic Principle in Cosmology, part 1 - Raphael Bousso

Entropy Bounds, Light-sheets, and the Holographic Principle in Cosmology, part 1 Raphael Bousso University of California, Berkeley July 28, 2011

From playlist PiTP 2011

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Linear Algebra 10f: The RREF of a Matrix Whose the Null Space is Known Beforehand

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

Related pages

Bonnor beam | Isometry group | Gravitational plane wave | Causal structure | Exact solutions in general relativity | Einstein field equations | Schwarzschild metric | Vaidya metric | Vacuum solution (general relativity) | Monochromatic electromagnetic plane wave | Neutrino | Vector field | Pp-wave spacetime | Stress–energy tensor | Einstein tensor | Lorentz group | Electrovacuum solution